If you are just in the early stages of your career then you may not even need a formal contract. A letter of agreement may be enough. If there is not a lot of money involved just send a letter of confirmation stating the date of the performance, the venue and the fee. A one page letter is all you need.

Later on you might need something more involved but for now I wouldn't bother.

I agree with Mark that you probably don't need a contract but there are a few things that you should make sure that you agree beforehand. Top of the list for me is some kind of cancellation fee. I've had gigs cancelled at late notice before now, a couple on the day of the performance and once the phone call came in about 20 minutes before I was due to leave the house. I offer a 50% cancellation fee which rises to 75% a week before the performance and then up to 90% on the day. Also collect payment before the performance, I ask for full payment a week before the gig. That'll help with a couple of things, it'll help you enforce the cancellation fee and avoids the awkward having to ask for payment moment if you're at a wedding or party.

I do bend the rules a little, corporate clients often like to be invoiced and will pay after the performance. That's usually ok but still be a little careful there, I've had to chase for my money with a few clients (and these were quite big companies too) and I've even got two for which I never received payment. I could have taken them to small claims but at the time I had quite a bit going on in my life and didn't need the bother so let it go.